$2\mathrm{.}8$ The velocity field given in Problem $2\mathrm{.}4$ is called vortex flow, which will be

discussed in Chapter $3.$ For vortex flow, calculate:

a$.$ The time rate of change of the volume of a fluid element per unit volume.

b$.$ The vorticity.

Hint: Again, for convenience use polar coordinates. $2\mathrm{.}4$ Consider a velocity field where the $x$ and $y$ components of velocity are

given by $u=c\frac{y}{x^2+y^2}$ and $v=-c\frac{x}{x^2+y^2},$ where $c$ is a constant.

Obtain the equations of the streamlines. SOLVE QUESTION $2\mathrm{.}8$ CLEARLY AND SHOW ALL WORK PLS$!!$ EXPLAIN WHAT EQUATIONS ARE USED AND WHY. THANK YOU!